Abstract

We present a phase-imaging technique to quantitatively study the three-dimensional structure of cells. The method, based on the simultaneous dual-wavelength digital holography, allows for higher axial range at which the unambiguous phase imaging can be performed. The technique is capable of nanometer axial resolution. The noise level, which increases as a result of using two wavelengths, is then reduced to the level of a single wavelength. The method compares favorably to software unwrapping, as the technique does not produce non-existent phase steps. Curvature mismatch between the reference and object beams is numerically compensated. The 3D images of SKOV-3 ovarian cancer cells are presented.

© 2008 Optical Society of America

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References

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  1. W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).
  2. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am.  A 11, 2011–2015 (1994).
    [Crossref]
  3. U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [Crossref] [PubMed]
  4. U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [Crossref]
  5. J. W. Goodman, Introduction to Fourier Optics, 2nd ed (New York, McGraw-Hill, 1996).
  6. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
    [Crossref] [PubMed]
  7. L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A  18, 1033–1045 (2001).
    [Crossref]
  8. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A  20, 1755–1762 (2003).
    [Crossref]
  9. L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
    [Crossref]
  10. W.S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
    [Crossref] [PubMed]
  11. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
    [Crossref] [PubMed]
  12. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).
    [Crossref]
  13. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [Crossref]
  14. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
    [Crossref] [PubMed]
  15. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π-ambiguity by multiple-wavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
    [Crossref] [PubMed]
  16. C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
    [Crossref] [PubMed]
  17. K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE 6162, 616203 (2006).
    [Crossref]
  18. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Realtime dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. D. Parshall and M. K. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
    [Crossref] [PubMed]
  21. M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer2006).
  22. N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express,  15, 9239–9247 (2007).
    [Crossref] [PubMed]
  23. A. Khmaladze and M. Kim, “Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography,” in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
    [Crossref]
  24. A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.
  25. A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.
  26. A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
    [Crossref] [PubMed]
  27. M. Born and E. Wolfe, Principles of Optics, (Pergamon, 1964).
  28. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
    [Crossref] [PubMed]

2008 (1)

2007 (3)

2006 (2)

K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE 6162, 616203 (2006).
[Crossref]

D. Parshall and M. K. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (4)

2002 (1)

U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

2001 (4)

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001).
[Crossref] [PubMed]

L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A  18, 1033–1045 (2001).
[Crossref]

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
[Crossref]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

1999 (1)

1998 (1)

1994 (2)

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am.  A 11, 2011–2015 (1994).
[Crossref]

U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

1992 (1)

Asundi, A. K.

Barty, A.

Bevilacqua, F.

Bingham, P.

K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE 6162, 616203 (2006).
[Crossref]

Blandón, A.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

Born, M.

M. Born and E. Wolfe, Principles of Optics, (Pergamon, 1964).

Boyer, K.

Cai, L. L.

L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A  18, 1033–1045 (2001).
[Crossref]

Castañeda, R.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

Cullen, D.

Dakoff, A.

De Nicola, S.

Depeursinge, C.

Emery, Y.

Ferraro, P.

Finizio, A.

Gass, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed (New York, McGraw-Hill, 1996).

Grilli, S.

Haddad, W.S.

Jericho, M. H.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

Jueptner, W.

W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).

Jueptner, W. P.

U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

Khmaladze, A.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

A. Khmaladze and M. Kim, “Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography,” in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[Crossref]

Kim, M.

A. Khmaladze and M. Kim, “Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography,” in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[Crossref]

Kim, M. K.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express,  15, 9239–9247 (2007).
[Crossref] [PubMed]

D. Parshall and M. K. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
[Crossref] [PubMed]

C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
[Crossref] [PubMed]

J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π-ambiguity by multiple-wavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
[Crossref] [PubMed]

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer2006).

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

Kreuzer, H. J.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

Kühn, J.

Laporta, P.

Lo, C. M.

Longworth, J. W.

Magro, C.

Mann, C. J.

C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
[Crossref] [PubMed]

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer2006).

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

Marquet, P.

Matsushima, K.

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A  20, 1755–1762 (2003).
[Crossref]

McPherson, A.

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

Meucci, R.

Miao, J.

Miccio, L.

Montfort, F.

Nugent, K. A.

Osellame, R.

Paganin, D.

Parshall, D.

Paturzo, M.

Peng, X.

Pierattini, G.

Restrepo-Martínez, A.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

Rhodes, C. K.

Roberts, A.

Schimmel, H.

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A  20, 1755–1762 (2003).
[Crossref]

Schnars, U.

U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am.  A 11, 2011–2015 (1994).
[Crossref]

U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).

Solem, J. C.

Tobin, K.

K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE 6162, 616203 (2006).
[Crossref]

Warnasooriya, N.

Wolfe, E.

M. Born and E. Wolfe, Principles of Optics, (Pergamon, 1964).

Wyrowski, F.

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A  20, 1755–1762 (2003).
[Crossref]

Xu, L.

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

Yu, L.

C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
[Crossref] [PubMed]

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer2006).

Yu, L. F.

L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A  18, 1033–1045 (2001).
[Crossref]

Appl. Opt. (7)

U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
[Crossref]

W.S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[Crossref] [PubMed]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
[Crossref] [PubMed]

D. Parshall and M. K. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
[Crossref] [PubMed]

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. 47, 3203–3210 (2008).
[Crossref] [PubMed]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
[Crossref] [PubMed]

J. Opt. Soc. Am (1)

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am.  A 11, 2011–2015 (1994).
[Crossref]

J. Opt. Soc. Am. (2)

L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A  18, 1033–1045 (2001).
[Crossref]

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A  20, 1755–1762 (2003).
[Crossref]

Meas. Sci. Technol. (1)

U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Proc. Natl. Acad. Sci.USA (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA 98, 11301–10305 (2001).
[Crossref] [PubMed]

Proc. SPIE (1)

K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE 6162, 616203 (2006).
[Crossref]

Other (7)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed (New York, McGraw-Hill, 1996).

W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).

A. Khmaladze and M. Kim, “Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography,” in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[Crossref]

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD),(Optical Society of America, 2008), paper DMB5.

M. Born and E. Wolfe, Principles of Optics, (Pergamon, 1964).

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer2006).

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Figures (9)

Fig. 1.
Fig. 1.

Multi-wavelength digital holography apparatus. The focal length of the lenses L21 and L22 are 17.5 cm and 10 cm respectively. The beams are collimated between L11 and L21 and between L12 and L22 and again are collimated after 20x OBJ1 microscope objective.

Fig. 2.
Fig. 2.

Two-wavelength hologram of a USAF resolution target: (a) digital hologram (640×480pixels) and (b) its Fourier spectrum of the hologram with the red and the green wavelengths first order components shown.

Fig. 3.
Fig. 3.

R is the wave’s radius of curvature centered at C, which can be determined experimentally for a given setup, r¯ is the vector from the center of the CCD matrix (point O) to an arbitrary point A, and r¯0 is the vector from the center of the CCD matrix to the projection of the center of curvature on the CCD matrix P. Here r ̄ = x 2 + y 2 , x and y are the coordinates of A and r ̄ 0 = x 0 2 + y 0 2 , x0 and y0 are the coordinates of P.

Fig. 4.
Fig. 4.

The reconstructed phase image of the USAF resolution target (a) without curvature correction and (b) with curvature correction applied. The images are 174×174 μm2 (450×450pixels).

Fig. 5.
Fig. 5.

(a). Phase map and height profile for λ=633 nm. (b). For comparison, AFM image and height profile of the same area.

Fig. 6.
Fig. 6.

Phase maps for (a) λ 1=532 nm and (b) λ 2=633 nm; (c) 3D rendering of synthetic dualphase map with beat wavelength Λ12=3334nm and (d) reduced noise fine map (the images are 174×174 μm2, 450×450 pixels and the vertical scale for (a) and (b) is in radians).

Fig. 7.
Fig. 7.

Confluent SKOV-3 ovarian cancer cells: (a) amplitude image, (b) reconstructed phase for λ=532 nm, (c) dual-wavelength coarse phase image and (d) 3D rendering of fine map. All images are 92×92 μm2 (240×240 pixels).

Fig. 8.
Fig. 8.

A single SKOV-3 cell: (a) reconstructed phase for λ=633 nm, (b) dual-wavelength coarse phase image, (c) 3D rendering of fine map and (d) line thickness profile. All images are 63.5×59 μm2 (165×153 pixels).

Fig. 9.
Fig. 9.

Comparison between optical and software unwrapping: (a) amplitude image; (b) single wavelength phase image, (c) coarse maps, (d) 3D rendering of the dual-wavelength fine phase map and (e) software unwrapped phase map. Images are 98×98 μm2 (256×256 pixels).

Equations (10)

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A 0 ( k x , k y ; 0 ) = E 0 ( x , y ; 0 ) exp [ i ( k x x + k y y ) ] dxdy
A ( k x , k y ; z ) = A 0 ( k x , k y ; 0 ) exp [ ik z z ] ,
E ( x , y ; z ) = A ( k x , k y ; z ) exp [ i ( k x x + k y y ) ] dk x dk y
d = CA CO = CP 2 + PA 2 CP 2 + PO 2
d = R 2 + r ̄ r ̄ 0 2 R 2 + r ̄ 0 2 = R 2 + ( x x 0 ) 2 + ( y y 0 ) 2 R 2 + x 0 2 + y 0 2
E ( x , y ; 0 ) = E 0 ( x , y ; 0 ) exp [ ik ( ± [ R 2 + ( x x 0 ) 2 + ( y y 0 ) 2 R 2 + x 0 2 + y 0 2 ] ) ]
k ( R 2 + r 2 R ) = kR [ 1 + r 2 R 2 1 ] = 2 πR λ [ 1 + r 2 2 R 2 1 ] = 2 π λ x 2 + y 2 2 R
h x y = λ 4 π ϕ x y
h x y = λ 4 π ϕ x y ( n n 0 )
Λ 12 = λ 1 λ 2 λ 1 λ 2

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